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				<h1 class="content-heading">
                [FJOI2014]树的重心                </h1>
                <p>时间限制：10s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：512MB</p>			</div>
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                                <h3>题目描述</h3><p><div>给定一个n个点的树，每个点的编号从1至n，问这个树有多少不同的连通子树，和这个树有相同的重心。</div>
<div>其中n个点的树指的是n个点的最小连通图，显然n个点的树有n-1条边，去掉这n-1条边中的任何一条，原图都不再联通，任意两个点之间由唯一一条路径相连。</div>
<div>对于一个树，树的重心定义为：删掉某点i后，若剩余k个连通分量，那么定义d(i)为这些连通分量中点的个数的最大值，所谓重心，就是使得d(i)最小的点i。</div>
<div>基于以上定义，一个树的重心可能会有一个或者两个，题中所要求的联通子树，其重心编号和个数必须和原树的完全一样。</div>
<div>找出给定的树中有多少联通的子树和这个树有相同的重心。</div>
<div></div>
<p></p></p><hr/><h3>输入格式</h3><p><div>第1行中给出正整数Q，表示该组数据中有多少组测试样例。</div>
<div>
<div>每组样例首先输入一个整数n (0 &lt; n &le;200)，表示该组样例中输入的树包含n个点，之后n-1行，每行输入两整数数x，y(1 &le; x, y &le; n)，表示编号为x的点和编号为y的点之间存在一条边，所有点的编号从1-n</div>
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<p></p></p><hr/><h3>输出格式</h3><p><div>首先输出样例编号，之后输出满足条件的子树的个数，由于这个数字较大，你只需要输出这个数字对10007取模后的结果，即mod 10007，详见输出示例，请严格按照输出实例中的格式输出</div>
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<p></p></p><hr/><h3>样例输入</h3><pre>3
2
1 2
3
1 2
2 3
5
1 2
1 3
2 4
2 5</pre><hr/><h3>样例输出</h3><pre>Case 1: 1
Case 2: 2
Case 3: 6</pre><hr/><h3>提示</h3><p><p>100%的数据满足Q&le;50，n&le;200。</p>
<p></p></p><hr/><h3>题目来源</h3><p>没有写明来源</p>
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